William is 12 years older than Ben. Nineteen years ago, William was 3 times as old as Ben. How old is Ben now?
Solution: We can use the given information to write down two equations that describe the ages of William and Ben. Let William's current age be $w$ and Ben's current age be $b$ The information in the first sentence can be expressed in the following equation: $w = b + 12$ Nineteen years ago, William was $w - 19$ years old, and Ben was $b - 19$ years old. The information in the second sentence can be expressed in the following equation: $w - 19 = 3(b - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to use our first equation for $w$ and substitute it into our second equation. Our first equation is: $w = b + 12$ . Substituting this into our second equation, we get the equation: $(b + 12)$ $-$ $19 = 3(b - 19)$ which combines the information about $b$ from both of our original equations. Simplifying both sides of this equation, we get: $b - 7 = 3 b - 57$ Solving for $b$ , we get: $2 b = 50$ $b = 25$.